You're conflating health issues with health care issues.
What health care system now implemented in any country, or proposed for implementation in America by anyone, controls how people eat, how much alcohol, tobacco, and other harmful drugs they consume, how often they exercise, how much they sleep, whether they provide healthy environments for their children, etc.?
Just as schools and teachers are simply one factor in educational outcomes, the medical system is simply one factor in health outcomes. You must consider lifestyle, environmental, and genetic/epigenetic factors to get a full picture. You must equalize for these factors - as far as this is possible - to fairly compare the effect of the medical system and associated policies alone on health outcomes in different countries.
Properly accounting for genetic and lifestyle differences in different sub-populations is largely taboo, and this prevents a fair comparison of medical systems across countries.
Edit: Consider this article by the CDC on infant mortality:
https://www.cdc.gov/reproductivehealth/MaternalInfantHealth/...
Over 23,000 infants died in the United States in 2016. The five leading causes of infant death in 2016 were:
Birth defects.
Preterm birth and low birth weight.
Sudden infant death syndrome.
Maternal pregnancy complications.
Injuries (e.g., suffocation).
While the medical system can intervene, these causes all seem far more dependent on genetics, the mother's (and to a lesser extent the father's) behavior during pregnancy and the infancy of the child.
In 2016, infant mortality rates by race and ethnicity were as follows:
Non-Hispanic black: 11.4;
American Indian/Alaska Native: 9.4;
Native Hawaiian or other Pacific Islander: 7.4;
Hispanic: 5.0;
Non-Hispanic white: 4.9;
Asian: 3.6
Compare white Americans with European countries, and the discrepancy drops significantly. There's something beyond the medical / health care system playing a role here.